Optimal control of electromagnetic wave displacement with an unknown velocity of propagation

The aim of this paper is to control an electromagnetic wave that penetrates in a medium with some missing information about its physical properties. The missing value of wave velocity of propagation leads us to use averaged control notion which is recently introduced by E. Zuazua, also the boundary Dirichlet condition is unknown which requires using the notion of no-regret control introduced by J. L. Lions. In this work, we combine these two techniques where we introduce the notion of averaged no-regret control to solve our optimal control problem with missing data. The averaged no-regret control will be characterised by an optimality system.     

Stabilization of exponentially unstable discrete-time linear systems by truncated predictor feedback

Predictor state feedback solves the problem of stabilizing a discrete-time linear system with input delay by predicting the future state with the solution of the state equation and thus rendering the closed-loop system free of delay. The solution of the state equation contains a term that is the convolution of the past control input with the state transition matrix. Thus, the implementation of the resulting predictor state feedback law involves iterative calculation of the control signal. A truncated predictor feedback law results when the convolution term in the state prediction is discarded. When the feedback gain is constructed from the solution of a certain parameterized Lyapunov equation, the truncated predictor feedback law has been shown to achieve asymptotic stabilization of a system that is not exponentially unstable in the presence of an arbitrarily large delay by tuning the value of the parameter small enough. In this paper, we extend this result to exponentially unstable systems. Stability analysis leads to a bound on the delay and a range of the values of the parameter for which the closed-loop system is asymptotically stable as long as the delay is within the bound. The corresponding output feedback result is also derived.     

Regional stabilization for infinite-dimensional systems

The purpose of this paper is to discuss an output stabilization problem for linear infinite dimensional systems--regional stabilizability--and consists in studying the asymptotic behaviour of a distributed system on a subregion of its evolution domain. So we give definitions and some properties of this kind of stability. Also, we concentrate on the determination of the control which ensures regional stabilizability on a subregion interior to the system domain, with bounded state on the residual part and minimizing a given cost of performance. The obtained results are illustrated by many examples and simulations.     

Energy methods for stability of bilinear systems with oscillatory inputs

A large body of recent literature has been devoted to the topic of motions of mechanical systems forced by oscillatory inputs (see, for example, References 7, 12, 15, 17 and 29). A common feature in most of this work (with Reference 7 being the exception) is that the results apply principally to kinematic problems, and the equations of motion do not involve drift terms. The main object of study in this paper is the class of bilinear control systems with oscillatory (periodic) inputs. We shall show that included in this class are models of mechanical system dynamics which are obtained through a process of reduction and linearization about operating points. In particular, we study the stability of such systems under high-frequency, periodic forcing. The averaged potential is defined for linearizations of the systems on the (reduced) configuration space, and it is shown that stable motions of the forced system are associated with minimum values of this quantity. We use both classical averaging theory as well as a novel geometric argument to provide parallel but independent assessments of the use of the averaged potential in carrying out a stability analysis. A salient feature of the geometric approach is that we are able to justify the use of an energy-like quantity to determine Lyapunov stability in conservative mechanical systems. This makes contact with a growing body of literature on the use of energy methods for stability and control design (e.g. References 7, 8, 18, 24, 26 and 27). We briefly describe the connection with previous work on the averaged potential.     

Adaptive model predictive control for a class of constrained linear systems based on the comparison model

This paper proposes an adaptive model predictive control (MPC) algorithm for a class of constrained linear systems, which estimates system parameters on-line and produces the control input satisfying input/state constraints for possible parameter estimation errors. The key idea is to combine the robust MPC method based on the comparison model with an adaptive parameter estimation method suitable for MPC. To this end, first, a new parameter update method based on the moving horizon estimation is proposed, which allows to predict an estimation error bound over the prediction horizon. Second, an adaptive MPC algorithm is developed by combining the on-line parameter estimation with an MPC method based on the comparison model, suitably modified to cope with the time-varying case. This method guarantees feasibility and stability of the closed-loop system in the presence of state/input constraints. A numerical example is given to demonstrate its effectiveness.     

Parameter Control of Genetic Algorithms by Learning and Simulation of Bayesian Networks — A Case Study for the Optimal Ordering of Tables

Parameter setting for evolutionary algorithms is still an important issue in evolutionary computation. There are two main approaches to parameter setting: parameter tuning and parameter control. In this paper, we introduce self-adaptive parameter control of a genetic algorithm based on Bayesian network learning and simulation. The nodes of this Bayesian network are genetic algorithm parameters to be controlled. Its structure captures probabilistic conditional (in)dependence relationships between the parameters. They are learned from the best individuals, i.e., the best configurations of the genetic algorithm. Individuals are evaluated by running the genetic algorithm for the respective parameter configuration. Since all these runs are time-consuming tasks, each genetic algorithm uses a small-sized population and is stopped before convergence. In this way promising individuals should not be lost. Experiments with an optimal search problem for simultaneous row and column orderings yield the same optima as state-of-the-art methods but with a sharp reduction in computational time. Moreover, our approach can cope with as yet unsolved high-dimensional problems.     

Adaptive hybrid control of manipulators on uncertain flexible objects

This paper presents an adaptive hybrid control approach for a robot manipulator to interact with its flexible object. Because of its flexibility, the object dynamics influence the robot's control system, and since it is usually a distributed parameter system, the object dynamics as seen from the robot change when the robot moves. The problem becomes further complicated such that it is difficult to decompose the robot's position and contact force control loops. In this paper, we approximate the object's distributed parameter model into a lumped 'position state-varying' model. Then, by using the well-known nonlinear feedback compensation, we decompose the robot's control space into a position control subspace and object torque control subspace. We design the optimal state feedback for the position control loop and control the robot's contact force through controlling the resultant torque of the object. We use the model-reference simple adaptive control strategy to control the torque control loop. We also study the problem on how to select a reasonable reference model for this control loop. Experiments of a PUMA robot interacting with an aluminum beam show the effectiveness of our approach.     

Simultaneous fault estimation and fault-tolerant tracking control for uncertain nonlinear discrete-time systems

This paper deals with simultaneous fault estimation and control for a class of nonlinear systems with parameter uncertainty, which is described by Takagi–Sugeno (T–S) fuzzy model with parameter uncertainties and unknown disturbance. In this paper, a fuzzy reference model is used to generate error dynamic for tracking control. By considering actuator fault as an auxiliary state vector, we construct an augmented error system and propose a fault estimator/controller to achieve simultaneous fault estimation and fault-tolerant tracking control. H_∞ approach is used in the design of estimator/controller to attenuate the effect of the unknown disturbance and parameter uncertainties. The design conditions are formulated into a set of linear matrix inequalities (LMIs), which can be efficiently solved. Finally, a pitch-axis nonlinear missile model is used to illustrate the effectiveness of the proposed method.     

异步电机离线参数辨识

异步电机矢量控制要求准确获得磁场定向,而磁场定向的精度取决于电机参数值.为了准确辨识出电机的参数,本文研究基于静止状态下异步电机T型等效电路模型,采用脉冲电压法,单相交流注入法取代传统堵转和空载试验,实现对异步电机参数的准确测量.仿真实验结果证明上述方法正确可靠,且得到了较高的辩识精度.     

Active identification for discrete-time nonlinear control. I.Output-feedback systems

The problem of controlling nonlinear systems with unknown parameters has received a great deal of attention in the continuous-time case. In contrast, its discrete-time counterpart remains largely unexplored, primarily due to the difficulties associated with utilizing Lyapunov design techniques in a discrete-time framework. Existing results impose restrictive growth conditions on the nonlinearities to yield global stability. In this paper, we propose a novel approach, which removes this obstacle and yields global stability and tracking for systems that can be transformed into an output-feedback canonical form, in which the nonlinearities depend only on the measured output, but are otherwise arbitrary. The main novelties of our design are: (i) the temporal and algorithmic separation of the parameter estimation task from the control task, and (ii) the development of an active identification procedure, which uses the control input to actively drive the system state to points in the state space that allow the orthogonalized projection estimator to acquire all the necessary information about the unknown parameters. We prove that our algorithm guarantees complete (for control purposes) identification in a finite time interval, whose maximum length we compute. Thus, the traditional structure of concurrent online estimation and control is replaced by a two-phase control strategy: first use active identification, and then utilize the acquired parameter information to implement any control strategy as if the parameters were known     

Near optimal regional investment using a simultaneous equation economic model

A region seeking development objectives should attempt to schedule public investment optimally between human resources and physical infrastructure. A regional growth model and a suitable objective function are presented. It is desired to calculate both the optimal public investment for nominal parameter values and the sensitivity of the optimal solution with respect to changes in parameter values. However, the system is not in state form, but is represented as a set of nonlinear simultaneous equations. For this case the necessary conditions for optimality are difficult to solve. The approach suggested here is to choose a nominal parameter value of economic significance for which the model may be put into state form. Then the existing optimally sensitive control algorithm may be used with some modifications to obtain a near optimal investment strategy for the simultaneous equation system when the parameter deviates from the nominal value. In general, the results indicate an emphasis on education and training expenditures. Sensitivity results indicate that the relative emphasis on long vs short run considerations (i.e. public investment vs consumption) depends on the growth rate parameters in the model.     

三相PWM变换器的鲁棒变结构控制

分析了三相脉冲宽度调制(Pulse width modulation, PWM)功率因数校正(Power factor correction, PFC)变换器的工作原理和数学模型. 针对现有控制方法在参数不确定及参数变化时性能变差的问题, 提出采用鲁棒变结构控制减小系统参数不确定性的影响, 同时采用渐缩滑动边界的方法减小了控制量的颤振. 仿真及实验结果表明, 与传统PI控制和反馈线性化方法相比, 本文方法不仅在标称参数时具有较好的动静态性能, 而且在系统参数发生变化时, 具有更强的鲁棒性.     

Digital self-triggered robust control of nonlinear systems

In this paper, we develop novel results on self-triggered control of nonlinear systems, subject to perturbations, and sensing/computation/actuation delays. First, considering an unperturbed nonlinear system with bounded delays, we provide conditions that guarantee the existence of a self-triggered control strategy stabilizing the closed-loop system. Then, considering parameter uncertainties, disturbances and bounded delays, we provide conditions guaranteeing the existence of a self-triggered strategy that keeps the state arbitrarily close to the equilibrium point. In both cases, we provide a methodology for the computation of the next execution time. We show on an example the relevant benefits obtained with this approach in terms of energy consumption with respect to control algorithms based on a constant sampling with a sensible reduction of the average sampling time.     

Sensors structures and regional detectability of parabolic distributed systems

In this paper, we deal with the linear infinite dimensional systems in a Hilbert space where the dynamics of the system is governed by strongly continuous semi-groups. We study the concept of asymptotic (exponential) regional detectability in connection with the structures of sensors for a class of parabolic distributed parameter systems. For different sensors structures, we give the characterization of the asymptotic (exponential) regional detectability in order that asymptotic (exponential) regional observability be achieved. Furthermore, we apply these results to the regional observer for distributed parameter diffusion systems.     

Interval arithmetic techniques for the design of controllers for nonlinear dynamical systems with applications in mechatronics

In this paper, we give an overview of interval arithmetic techniques for both the offline and online verification of robust control strategies. Part 1 of the paper mainly addresses basic interval techniques focusing on offline applications while the focus of Part 2 is their online application. For offline applications, we aim at computing the sets of all admissible control strategies. Admissibility is defined in terms of constraints on, for example, the trajectories of the state variables, the range of control inputs, and the frequency response or eigenvalue regions of linear closed-loop control systems. In contrast to the offline application, the foremost requirement for online applications is the verification of the admissibility of at least one control strategy and to determine a suitable approximate solution to a control task which is both feasible and optimal in some specified sense. In addition to open-loop as well as closed-loop control, the problem of state and parameter estimation is addressed.     

Actuators and regional boundary controllability of parabolic systems

The purpose of this paper is to explore the boundary regional controllability concept in connection with the choice of actuators. First, we give a definition and some properties of this concept, then we concentrate on the determination of control achieving boundary regional controllability with minimum energy. We also give an important approach that leads to numerical implementation for the computation of the optimal control.     

State estimation and parameter identification method for dual-rate system based on improved Kalman prediction

For the dual-rate system, such as the process of space teleoperation whose control signals is partly determined by delayed feedback states, the state values and system parameters are coupled and influenced each other, which are hard to be estimated simultaneously. In this paper, we propose a novel method for this problem. Firstly, considering the asynchronism of the input and output sampling signals, an auxiliary model is modeled as a medium to the state and output functions. Secondly, the Kalman prediction algorithm is improved to estimate the state values at output signals of the dual-rate system. The general step is using the output estimated errors in original and auxiliary systems to modify the estimated state values of the auxiliary model, and then the unknown state values in original system is defined by the ones in auxiliary model. Based on improved Kalman algorithm and hierarchical identification algorithm, we present the detailed procedures of state estimation and parameter identification method for the dual-rate system. The processes of state estimation and parameter identification are calculated and modified alternately. Finally, the simulation results reveal that the state and parameters both approach to the real values and the state values converge faster than the parameters.     

Target mass control for uncertain compartmental systems

In this article we analyse the total mass target control problem for compartmental systems under the presence of parameter uncertainties. We consider a state feedback control law with positivity constraints tuned for a nominal system, and prove that this law leads the value of the total mass of the real system to an interval whose bounds depend on the parameter uncertainties and can be made arbitrarily close to the desired value of the total mass when the uncertainties are sufficiently small. Moreover, we prove that for a class of compartmental systems in ?³ of interest, the state of the controlled system tends to an equilibrium point whose total mass lies within the aforementioned interval. Taking into account the relationship between the mass and the state components in steady state, it is possible to use the proposed mass control law to track the desired values for the steady state components. This is applied to the control of the neuromuscular blockade level of patients undergoing surgery, by means of the infusion of atracurium. Our results are illustrated by several simulations and a clinical case.     

A constrained tracking control algorithm for linear systems based on a spline‐type parameter‐dependent Lyapunov function

In this paper, we propose a design method of a tracking control law for discrete‐time linear systems with actuator saturation. The feedback gain of the control law is actively changed online so that the control performance is improved based on the information of the state variable and the reference signal. The control law is designed with considering the rate of convergence of the tracking error. The design condition of the control law is derived as polynomially parameter‐dependent matrix inequalities, and a spline‐type parameter‐dependent Lyapunov function and a convex polytope are used to reduce the design condition to a finite number of LMIs. Three numerical examples are provided to illustrate effectiveness of the method. Copyright © 2014 John Wiley & Sons, Ltd.